Recent years have witnessed a booming interest in the data-driven paradigm
for predictive control. However, under noisy data ill-conditioned solutions
could occur, causing inaccurate predictions and unexpected control behaviours.
In this article, we explore a new route toward data-driven control of
stochastic systems through active offline learning of innovation data, which
gives an answer to the critical question of how to derive an optimal
data-driven model from a noise-corrupted dataset. A generalization of the
Willems' fundamental lemma is developed for non-parametric representation of
input-output-innovation trajectories, provided realizations of innovation are
precisely known. This yields a model-agnostic unbiased output predictor and
paves the way for data-driven receding horizon control, whose behaviour is
identical to the ``oracle" solution of certainty-equivalent model-based control
with measurable states. For efficient innovation estimation, a new low-rank
subspace identification algorithm is developed. Numerical simulations show that
by actively learning innovation from input-output data, remarkable improvement
can be made over present formulations, thereby offering a promising framework
for data-driven control of stochastic systems